Abstract

An analysis of the depth of field (DOF) of the wavefront coding imaging system with a cubic phase mask is presented. A necessary condition on the base of that MTF of wavefront coding system is defocus-independent is described. Then the extension ratio of the DOF relative to that of traditional optical system is calculated. And the conclusion is also verified by the simulation results.

© 2008 Optical Society of America

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References

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  1. E. R. Dowski and W. T. Cathey, "Extended depth of field through Wavefront Coding," Appl. Opt. 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
  2. S. C. Tucker, W. T. Cathey, and E. R. Dowski, "Extended depth of field and aberration control for inexpensive digital microscope systems," Opt. Express 4, 467-474 (1999).
    [CrossRef] [PubMed]
  3. H. Wach, E. R. Dowski, and W. T. Cathey, "Control of Chromatic Focal Shift through Wavefront Coding," Appl. Opt. 37, 5359-5367 (1998).
    [CrossRef]
  4. S. Bradburn, E. R. Dowski, and W. T. Cathey, "Realizations of Focus Invariance in Optical-Digital Systems with Wavefront Coding," Appl. Opt. 36, 9157-9166(1997).
    [CrossRef]
  5. D. L. Marks, R. A. Stack, and D. J. Brady, "Three-dimensional Tomography using a Cubic-Phase Plate Extended Depth-of-Field System," Opt. Lett. 24, 253-255 (1999).
    [CrossRef]
  6. R. Narayanswamy, G. E. Johnson, P. E. X. Silveira, and H. B. Wach, "Extending the imaging volume for biometric iris recognition," Appl. Opt. 44, 701-712 (2005).
    [CrossRef] [PubMed]
  7. R. Plemmons, M. Horvath, E. Leonhardt, P. Pauca, S. Prasad, S. Robinson, H. Setty, T. Torgersen, J. Gracht, E. Dowski, R. Narayanswamy, and P. E. X. Silveir, "Computational Imaging Systems for Iris Recognition," Proc. SPIE 5559 346-357.
  8. P. E. X. Silveira and R. Narayanswamy, "Signal-to-noise analysis of task-based imaging systems with defocus," Appl. Opt. 45, 2924-2934 (2006).
    [CrossRef] [PubMed]
  9. E. R. Dowski and G. E. Johnson, "Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems," Proc. SPIE 3779, 137-145 (1999).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics, 3rd Ed. (New York: Roberts and Company Publishers Inc., 2005), p128.

2006 (1)

2005 (1)

1999 (3)

1998 (1)

1997 (1)

1995 (1)

Bradburn, S.

Brady, D. J.

Cathey, W. T.

Dowski, E. R.

Johnson, G. E.

R. Narayanswamy, G. E. Johnson, P. E. X. Silveira, and H. B. Wach, "Extending the imaging volume for biometric iris recognition," Appl. Opt. 44, 701-712 (2005).
[CrossRef] [PubMed]

E. R. Dowski and G. E. Johnson, "Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems," Proc. SPIE 3779, 137-145 (1999).
[CrossRef]

Marks, D. L.

Narayanswamy, R.

Silveira, P. E. X.

Stack, R. A.

Tucker, S. C.

Wach, H.

Wach, H. B.

Appl. Opt. (5)

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

E. R. Dowski and G. E. Johnson, "Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems," Proc. SPIE 3779, 137-145 (1999).
[CrossRef]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 3rd Ed. (New York: Roberts and Company Publishers Inc., 2005), p128.

R. Plemmons, M. Horvath, E. Leonhardt, P. Pauca, S. Prasad, S. Robinson, H. Setty, T. Torgersen, J. Gracht, E. Dowski, R. Narayanswamy, and P. E. X. Silveir, "Computational Imaging Systems for Iris Recognition," Proc. SPIE 5559 346-357.

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Figures (6)

Fig. 1.
Fig. 1.

MTF of traditional and wavefront coding optical system.

Fig. 2.
Fig. 2.

The original image of Sector Star Target

Fig. 3.
Fig. 3.

Images of the Sector Star Target from a traditional imaging system. The best focus image is given in (a), defocus of 2 depth of focus result in (b) and defocus of 30 depth of focus result in (c).

Fig. 4.
Fig. 4.

Images of the Sector Star Target from a Wavefront Coded system before filtering. The best focus image is given in (a), defocus of 30 depth of focus result in (b) and defocus of 60 depth of focus result in(c).

Fig. 5.
Fig. 5.

Images of the Sector Star Target from a Wavefront Coded system after filtering. The best focus image is given in (a), defocus of 30 depth of focus result in (b), and defocus of 60 depth of focus result in (c).

Fig. 6.
Fig. 6.

Images of the Sector Star Target from a Wavefront Coded system are shown. Defocus of 65 DOF result in a and b, a is before filtering and b is after filtering; And defocus of 100 depth of focus result in c and d, c is before filtering and d is after filtering.

Equations (21)

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p ( x , y ) = { 1 2 exp [ j α ( x 3 + y 3 ) ] x 1 , y 1 0 otherwise
ε = 1 d i + Δ 1 d i Δ d i 2
W 20 = ε L 2 8
Δ 2 λ d i 2 L 2
H ( f x ) = 1 L P ( x + λ d i f x 2 ) P * ( x λ d i f x 2 ) exp ( j 2 π 8 d i f x W 20 L 2 x ) d x
p ( x ) = { 1 2 exp ( j α x 3 ) x L 2 0 otherwise
α = 8 α L 3
H ( f x ) = 1 2 L rect ( x L λ d i f x ) exp ( j [ α λ d i f x ( 3 x 2 + 1 4 λ 2 d i 2 f x 2 ) + 2 π 8 d i f x W 20 L 2 x ] ) d x
f ( x ) = α λ d i f x ( 3 x 2 + 1 4 λ 2 d i 2 f x 2 ) + 2 π 8 d i f x W 20 L 2 x
g ( x ) = rect ( x L λ d i f x )
x 0 = 8 π W 20 3 α λ L 2
f ( x ) = f ( x 0 ) + 1 2 f ( x 0 ) ( x x 0 ) 2
H ( f x ) = 1 2 L 2 π k f ( x 0 ) g ( x 0 ) exp { j [ k f ( x 0 ) + π 4 ] }
H ( f x ) = 1 2 L π 3 α λ d i f x exp ( j α λ 3 d i 3 f x 3 4 ) exp ( j 64 π 2 d i f x W 20 2 9 α λ L 4 )
x 0 L λ d i f x 2
W 20 3 α λ 2 π ( 1 λ d i f x L )
2 Δ d i 2 24 α λ ( 1 λ d i f x L ) π L 2
M = 6 α ( 1 λ d i f x L ) π
f x L λ d i ( π M 6 α 1 )
f c = L 2 λ d i
M = 3 α π

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